Gödel, Escher, Bach An Eternal Golden Braid by Douglas R. Hofstadter

sion that there is some sort of partial software isomorphism connecting the

brains of people whose style of thinking is similar-in particular, a corre-

spondence of (1) the repertoire of symbols, and (2) the triggering patterns

of symbols.

Comparing Different Semantic Networks

But what is a partial isomorphism? This is a most difficult question to

answer. It is made even more difficult by the fact that no one has found an

adequate way to represent the network of symbols and their triggering

patterns. Sometimes a picture of a small part of such a network of symbols

is drawn, where each symbol is represented as a node into which, and out of

which, lead some arcs. The lines represent triggering relationships-in

some sense. Such figures attempt to capture something of the intuitively

sensible notion of "conceptual nearness". However, there are many differ-

ent kinds of nearness, and different ones are relevant in different contexts.

A tiny portion of my own "semantic network" is shown in Figure 70. The

problem is that representing a complex interdependency of many symbols

cannot be carried out very easily with just a few lines joining vertices.

Another problem with such a diagram is that it is not accurate to think

of a symbol as simply "on" or "off". While this is true of neurons, it does

not carry upwards, to collections of them. In this respect, symbols are quite

a bit more complicated than neurons-as you might expect, since they are

made up of many neurons. The messages that are exchanged between

symbols are more complex than the mere fact, "I am now activated". That

is more like the neuron-level messages. Each symbol can be activated in

many different ways, and the type of activation will be influential in deter-

mining which other symbols it tries to activate. How these intertwining

triggering relationships can be represented in a pictorial manner-indeed,

whether they can be at all-is not clear.

But for the moment, suppose that issue had been solved. Suppose we

now agree that there are certain drawings of nodes, connected by links (let

us say they come in various colors, so that various types of conceptual

nearness can be distinguished from each other), which capture precisely

the way in which symbols trigger other symbols. Then under what condi-

tions would we fee! that two such drawings were isomorphic, or nearly

isomorphic? Since we are dealing with a visual representation of the net-

work of symbols, let us consider an analogous visual problem. How would

you try to determine whether two spiderwebs had been spun by spiders

belonging to the same species? Would you try to identify individual vertices

which correspond exactly, thereby setting up an exact map of one web onto

the other, vertex by vertex, fiber by fiber, perhaps even angle by angle?

This would be a futile effort. Two webs are never exactly the same; yet

there is still some sort of "style", "form", what-have-you, that infallibly

brands a given species' web.

In any network-like structure, such as a spiderweb, one can look at

local properties and global properties. Local properties require only a very

Minds and Thoughts^371